Value-free reductions

• 成果类型: Article
• 署名作者: Perez-Castrillo, David; Sun, Chaoran
• 署名单位: Autonomous University of Barcelona
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2021.09.009
• 发表日期: 2021
• 页码: 543-568
• 关键词: Coalitional games; Reduced games; Axiomatization; Consistency; Shapley value; Duality

摘要

We introduce the value-free (v-f) reductions, operators that map a coalitional game played by a set of players to another similar game played by a subset of those players. We propose properties that v-f reductions may satisfy, we provide a theory of duality, and we characterize several v-f reductions (among which the value-free version of the reduced games proposed by Hart and Mas-Colell, 1989, and Oishi et al., 2016). Unlike reduced games, introduced to characterize values in terms of consistency, v-f reductions are not defined in reference to values. However, a v-f reduction induces a value. We characterize v-f reductions that induce the Shapley, the stand-alone, and the Banzhaf values. We connect our approach to the theory of implementation. Finally, our new approach is a valuable tool to provide new characterizations of values in terms of consistency. We present new characterizations of the Banzhaf and the stand-alone values. (C) 2021 Elsevier Inc. All rights reserved.